23.5.92 problem 92

Internal problem ID [6701]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 92
Date solved : Friday, October 03, 2025 at 02:09:46 AM
CAS classification : [[_3rd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} y+x y^{\prime }+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime \prime }+x \left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime \prime }&=f \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 1308

ode:=y(x)+x*diff(y(x),x)+(b1*x+a1)*diff(diff(y(x),x),x)+x*(b0*x+a0)*diff(diff(diff(y(x),x),x),x) = f(x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✓ Mathematica. Time used: 3.947 (sec). Leaf size: 1610

ode=y[x] + x*D[y[x],x] + (a1 + b1*x)*D[y[x],{x,2}] + x*(a0 + b0*x)*D[y[x],{x,3}] == f[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
a0 = symbols("a0") 
a1 = symbols("a1") 
b0 = symbols("b0") 
b1 = symbols("b1") 
y = Function("y") 
ode = Eq(x*(a0 + b0*x)*Derivative(y(x), (x, 3)) + x*Derivative(y(x), x) + (a1 + b1*x)*Derivative(y(x), (x, 2)) - f(x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-a1*Derivative(y(x), (x, 2)) - x*(a0*Deri